CONTROL OF MARKOV JUMP LINEAR SYSTEMS WITH STATE AND INPUT CONSTRAINTS: A NECESSARY OPTIMALITY CONDITION

This paper presents necessary optimality conditions for the control problem of discrete-time Markov jump linear systems (M JLS) with linear feedback gains, subject to constraints on the system state and input control variables. Instead of hard, deterministic constraints, the constraints considered here are given in terms of the first and second moments of the state and input variables, thus adequate to in the stochastic setting. The jumping state of the Markov chain and the continuous part of the MJLS are assumed to be accessible to the controller. The necessary conditions are derived and they are attained numerically by means of a method that iteratively performs a variational search using a set of LMI's. It searches through monotonically decreasing costs and converges to a sequence of feedback gains that satisfies the optimality conditions. The usefulness of the method is illustrated by a numerical example.